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JEE MainChemistrySolid State

In a crystalline solid compound, atoms of element Y form a ccp lattice and atoms of element X occupy 1 3 of the octahedral voids. The empirical formula of the compound is expressed with the simplest whole-number stoichiometry. The total number of unoccupied octahedral voids in 0.5 mol of this compound is x 10²¹ . The value of x is _____. (Given N_A = 6.02 10²³ mol ⁻¹ )

Correct answer

602

Step-by-step solution

Let the number of atoms of Y in the ccp lattice be N . The number of octahedral voids generated is N . Since atoms of X occupy 1 3 of the octahedral voids, the number of X atoms is N 3 . The molar ratio of X to Y is 1 3 : 1 = 1 : 3 . Thus, the simplest empirical formula of the compound is XY ₃ . In 1 mol of XY ₃ , there are 3 mol of Y atoms. In 0.5 mol of the compound, the number of moles of Y atoms = 0.5 3 = 1.5 mol . The total number of octahedral voids is equal to the number of lattice-forming atoms ( Y ), which

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